In previous efforts a complete but unwieldy theory has been developed to account for and correct distortions in probe microscope or profilometer data (R. Chicon, M. Ortuno, and J. Abellan Surface Science vol. 181, p. 107ff (1987), P. Niedermann and O. Fischer, Journal of Microscopy vol. 152, p. 93ff (1988), G. Riess, F. Schneider, J. Vancea, and H. Hoffmann Applied Physics Letters vol. 57, p867ff (1990), D. Keller, Surface Science vol. 253, p. 353ff (1991), see attached reprint 1). In these prior efforts, corrections to the experimentally gathered data are computed (in the most general case) with Legendre transforms (or something equivalent) of the image and tip surfaces. Legendre transforms require numerical derivatives of the data, which are notoriously sensitive to noise.
It is possible in principle to remove some of this noise by standard smoothing techniques. But smoothing eliminates all the sharp features in an image, and in the case of probe images, certain types of sharp features are crucial to provision of accurate and correct reconstruction. As a result, even minimal smoothing tends to cause false reconstructions. Also, experience has been that very strong smoothing is often needed to reduce the noise enough to allow meaningful reconstruction.
As a result, relatively few applications of the previous approaches have been attempted, and these have provided data from relatively large samples where noise is minimized. The new arrangement of the present invention does not require the use of Legendre transforms or numerical derivatives, and is very insensitive to noise. When reconstructions using both the prior methods and the arrangement of the present invention are compared, the arrangement of the invention provides superior results, even in cases where noise is low.